"I think he's considering perhaps terminating the special counsel. I think he's weighing that option," said Ruddy, a close Trump ally, told PBS NewsHour on Monday. "I think it's pretty clear by what one of his lawyers said on television recently."

But letting Mueller go would "be a very significant mistake," Ruddy continued.

Such a decision could have disastrous political ramifications for Trump, who's already fending off accusations that he fired former FBI Director James Comey in order to stifle that same investigation. The probe is looking into links between the Trump campaign and the Kremlin.

In an interview with ABC News on Sunday, Trump attorney Jay Sekulow said he didn't want to speculate on whether the president would fire Mueller.

PBS anchor Judy Woodruff first tweeted the news. Earlier on Monday, CNBC spotted Ruddy leaving the West Wing. Ruddy, however, did not meet with the president as their meeting was postponed, NBC News reported.

Later on Monday night, White House Press Secretary Sean Spicer issued a statement saying Ruddy never spoke to the president, adding that only the "president or his attorneys are authorized to comment."

In a statement to NBC News, Ruddy indicated that Spicer's statement wasn't relevant, because he never claimed to have spoken to Trump about Mueller in the first place.

"Don't waste your time trying to undermine one of your few allies," the statement said.

Sessions is next on deck for Senate

Comey, who was conducting an inquiry into possible collusion between Trump's presidential campaign and Moscow, said in testimony last week that the president had referred to the investigation as "a cloud" over his administration. He alleged that Trump asked him for loyalty and requested that he drop an investigation into former national security advisor Michael Flynn, which Trump has denied.